In this paper we consider a geometric inverse problem
which requires detecting an unknown obstacle such as a submarine or
an aquatic mine immersed in a Stokes slow viscous stationary flow of
an incompressible fluid, from a single set of Cauchy (fluid velocity
and stress force) boundary measurements. The numerical
reconstruction is based on the method of fundamental solutions (MFS)
for the pressure and streamfunction in two dimensions combined with
regularization. Numerical results are presented and discussed.